# A greedy non-intrusive reduced order model for shallow water equations

arXiv: https://arxiv.org/abs/2002.11329 · HTML: https://mlsanity.com/paper/2002.11329/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2020.

## Built on by (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics](https://mlsanity.com/paper/2104.13962/) (2021)
- [Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation](https://mlsanity.com/paper/2210.14764/) (2022)
- [Active-Learning-Driven Surrogate Modeling for Efficient Simulation of Parametric Nonlinear Systems](https://mlsanity.com/paper/2306.06174/) (2023)
- [Efficient Deconvolution in Populational Inverse Problems](https://mlsanity.com/paper/2505.19841/) (2025)
- [Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs](https://mlsanity.com/paper/2107.02784/) (2021)
- [A Neural Operator Emulator for Coastal and Riverine Shallow Water Dynamics](https://mlsanity.com/paper/2502.14782/) (2025)
- [Deep Convolutional Architectures for Extrapolative Forecast in Time-dependent Flow Problems](https://mlsanity.com/paper/2209.09651/) (2022)
- [Physics-based Reduced Order Modeling for Uncertainty Quantification of Guided Wave Propagation using Bayesian Optimization](https://mlsanity.com/paper/2307.09661/) (2023)
- [Spatially-Enhanced Temporal Fusion Transformer: Interpretable Multi-Output Prediction for Parametric Dynamical Systems with Time-Varying Inputs](https://mlsanity.com/paper/2505.00473/) (2025)
- [Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction](https://mlsanity.com/paper/2606.06385/) (2026)
- [Greedy feature selection: Classifier-dependent feature selection via greedy methods](https://mlsanity.com/paper/2403.05138/) (2024)
- [Finetuning greedy kernel models by exchange algorithms](https://mlsanity.com/paper/2404.19487/) (2024)

## Abstract (arXiv)

In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function (RBF) interpolation method to construct efficient reduced order models for time-dependent problems arising in large scale environmental flow applications. The performance of the POD-RBF NIROM is compared with a traditional nonlinear POD (NPOD) model by evaluating the accuracy and robustness for test problems representative of riverine flows. Different greedy algorithms are studied in order to determine a near-optimal distribution of interpolation points for the RBF approximation. A new power-scaled residual greedy (psr-greedy) algorithm is proposed to address some of the primary drawbacks of the existing greedy approaches. The relative performances of these greedy algorithms are studied with numerical experiments using realistic two-dimensional (2D) shallow water flow applications involving coastal and riverine dynamics.